Definition:Angular Measure/Radian

Definition

The radian is the SI unit of plane angle.

It can be symbolized either by the word $\radians$ or without any unit.

Radians are pure numbers, as they are ratios of lengths. The addition of $\radians$ is merely for clarification.

$1 \radians$ is the angle subtended at the center of a circle by an arc whose length is equal to the radius:

Value of Radian in Degrees

The value of a radian in degrees is given by:

$1 \radians = \dfrac {180 \degrees} {\pi} \approx 57 \cdotp 29577 \, 95130 \ 82320 \, 87679 \, 8154 \ldots \degrees$

This sequence is A072097 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

Also known as

Radian measure is also known as circular measure.

Also see

• Measurement of Full Angle

• Definition:Steradian

• Results about radians can be found here.

Technical Note

The $\LaTeX$ code for \(\radians\) is \radians .

Sources

• 1976: K. Weltner and W.J. Weber: Mathematics for Engineers and Scientists ... (previous) ... (next): $1$. Functions: $1.5$ Trigonometric or Circular Functions: $1.5.1$ Unit Circle
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): angular measure
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): radian
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): angular measure
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): radian
• 2008: Ian Stewart: Taming the Infinite ... (previous) ... (next): Chapter $5$: Eternal Triangles: The origins of trigonometry
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): angle (angular)

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